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d is clear from the context, then we write g i,j for g d,i,j . G is called L -uniformly compressibly SENS if, moreover,
We give lower bounds on the complexity of the word problem for a large class of non-solvable infinite groups that we call strongly efficiently non-solvable groups. This class includes free groups, Grigorchuk’s group, and Thompson’s groups. We prove that these groups have an NC1-hard word problem and that for some of them (including Grigorchuk’s group and Thompson’s groups) the compressed word problem (which is equivalent to the circuit evaluation problem) is PSPACE-complete.
ACM Transactions on Computation Theory (TOCT) – Association for Computing Machinery
Published: Feb 1, 2023
Keywords: NC1-hardness
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